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SET THEORY AND LOGICPROBLEM SET NUMBER 1RICHARD B. PAULINO1

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RICHARD B. PAULINO2Problem # 1.Use the set notation for the following statements: a. The set of all pairs of numbers a and b, being a an integer and b a real number A = { (a,b)|a Є b Є R } b. x is a member of the set A B = { x|x Є A } c. A is the set of the vowels of English Alphabet A = { x|x is a vowel in the english alphabet }

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RICHARD B. PAULINO3Problem #2.Write the following in tabular form a. A = { x|x+3=9} A= { 6 } b. D= { x|x is a number of two digits divisible by 7}D = A= { 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98 }Problem #3.Which of the following sets are equal? a. { x|x is a letter in the word mathematics} b. A set containing m,a,t,h,e,i,cand s c. A set of letters containing the word manuscript. a and b are equal setsProblem #4. Which of these sets is/are null set(s)? A = { x|x is a a letter after Z in the alphabet}B = { x|x2 = 4 and x = 1}C = { x| x + 9 = 9}D = { x|x≥4 and x<1 }Sets A, B and D are null sets

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RICHARD B. PAULINO4Problem #5. Which sets are subsets of the others? A = { x|x is a Quadrilateral} B = { x|x is a rhombus} C = { x|x is a rectangle} D = { x|x is a square}

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RICHARD B. PAULINO5Problem #6. State whether each of the following sets is infinite or finite.a. The set of lines parallel to y-axis b. The set of articles through the originc. The roots of the equation (x-1)(x-2)(x-3)d. The set of number & which are multiple of 7a. infiniteb. finitec. infinited. infinite

Problem #7. Write true or false for the following statements if A = {1, {4,5}, 4} a. {4,5} A a. FALSE b. {{4,5}} A b. TRUE

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RICHARD B. PAULINO9Problem #10. In a certain school 80 students went to the zoo with hamburger, milk and cake with breakdown us follows: 2 had hamburger and milk 6 had cake & milk 12 had cake & hamburger 36 had cake 22 had milka. How many had nothing? b. How many had cake?c. How many had hamburger and cake? d. How many had hamburger and milke. How many had hamburger only? f. How many had milk only? g. How many had milk and cake?